We consider the problem of classification of invariant subspaces for the class of uniform Jordan operators. We show that given two invariant subspaces $M_1$ and $M_2$ of a uniform Jordan operator $T=S(\theta)\oplus S(\theta)\oplus \ldots$, the subspace $M_2$ belongs to the quasiaffine orbit of $M_1$ if and only if the restrictions $T|M_1$ and $T|M_2$ are quasisimilar and the compression $T_{ M_2^\perp}$ can be injected in the compression $T_{ M_1^\perp}$. Our result refines previous work on the subject by Bercovici and Smotzer.
Categories: math.FA math.OA